JQuery .js files

JQuery .js files

I noticed there are multiple .js files for JQuery. What are the differences and do I need to include all of them in my HTML? I have a process moving an item from one listbox to another that I cannot get to work yet someone else has it working. But he has a ton of other .js files in his code. I do not know if I need to add all of them or there is some other error. I have attached the stripped own code which I cannot get to work either. Don't know what I am doing wrong. I LOVE JQuery but find it difficult at times.

I appreciate any answers to help me understand JQuery and to figure out what I am doing wrong. Thanks for any and all replies.

Mike